Question

The rms speed of oxygen at room temperature is about \(500 \, \text{m/s}\). The rms speed of hydrogen at the same temperature is about

• A. \(125 \, \text{m/s}\)
• B. \(2000 \, \text{m/s}\)
• C. \(8000 \, \text{m/s}\)
• D. \(500 \, \text{m/s}\)

Hint:

Use \( v_{\text{rms}} \propto \frac{1}{\sqrt{M}} \) when comparing speeds of gases at the same temperature.

Answer 1

The Correct Option is B

The root mean square (rms) speed of a gas is inversely proportional to the square root of its molar mass: \[ v_{\text{rms}} \propto \frac{1}{\sqrt{M}} \] Let: - \( M_O = 32 \, \text{g/mol} \) (Oxygen)
- \( M_H = 2 \, \text{g/mol} \) (Hydrogen)
- \( \frac{v_H}{v_O} = \sqrt{\frac{M_O}{M_H}} = \sqrt{\frac{32}{2}} = \sqrt{16} = 4 \)
So, \[ v_H = 4 \times v_O = 4 \times 500 = 2000 \, \text{m/s} \]